Problem: Rewrite as a simplified fraction. ${3.\overline{60} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 360.606...\\ 1x &= 3.606...\end{align*}}$ Subtracting the two equations, we have: ${99x = 357}$ ${x = \dfrac{357}{99}} $ ${x = \dfrac{119}{33}} \text{or} {3 \dfrac{20}{33}}$